Program Requirements
Students may complete this program with a minimum of 18 credits or a maximum of 20 credits.
Taken together with the B.A.; Major Concentration in Statistics, this program constitutes an equivalent of the B.Sc.; Major in Statistics program offered by the Faculty of Science. It provides training in statistics, with a mathematical core and basic training in computing. With satisfactory performance in an appropriate selection of courses, these two programs can lead to the accreditation "A.Stat" from the Statistical Society of Canada, which is regarded as the entry level requirement for a statistician practicing in Canada.
This supplementary minor concentration is open only to students registered in the B.A.; Major Concentration in Statistics. Taken together, these two programs constitute a program equivalent to the B.Sc.; Major in Statistics offered by the Faculty of Science. No course overlap between the B.A.; Major Concentration in Statistics and the B.A.; Supplementary Minor Concentration in Statistics is permitted.
Note that according to the Faculty of Arts Multi-Track System degree requirements, option C, students registered in the B.A.; Supplementary Minor Concentration in Statistics must also complete another minor concentration in a discipline other than Mathematics and Statistics. For more information about the Multi-Track System options, please refer to Faculty of Arts regulations under "Faculty Degree Requirements," "About Program Requirements," and "Departmental Programs."
Guidelines for Course Selection
Students are strongly advised to complete all required courses and all Part I and Part II complementary courses
by the end of U2, except for MATH 423.
Where appropriate, Honours courses may be substituted for equivalent courses. Students planning to pursue graduate studies are encouraged to make such substitutions, and to take MATH 556 and MATH 557 as complementary courses.
Required Courses (6 credits)
* If MATH 423 has been taken as part of the B.A.; Major Concentration in Statistics, another 3-credit
complementary course from Part II must be taken.
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MATH 243 Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Terms: Winter 2025
Instructors: Hundemer, Axel (Winter)
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MATH 423 Applied Regression (3 credits) *
Overview
Mathematics & Statistics (Sci) : Multiple regression estimators and their properties. Hypothesis tests and confidence intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data.
Terms: Fall 2024
Instructors: Steele, Russell (Fall)
Complementary Courses (12-14 credits)
Part I: 3 credits selected from **:
** Students who have sufficient knowledge in programming are encouraged to take COMP 250.
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COMP 202 Foundations of Programming (3 credits)
Overview
Computer Science (Sci) : Introduction to computer programming in a high level language: variables, expressions, primitive types, methods, conditionals, loops. Introduction to algorithms, data structures (arrays, strings), modular software design, libraries, file input/output, debugging, exception handling. Selected topics.
Terms: Fall 2024, Winter 2025, Summer 2025
Instructors: M'hiri, Faten (Fall) M'hiri, Faten (Winter)
3 hours
Restrictions: Not open to students who have taken or are taking COMP 204, COMP 208, or GEOG 333; not open to students who have taken or are taking COMP 206 or COMP 250.
COMP 202 is intended as a general introductory course, while COMP 204 is intended for students in life sciences, and COMP 208 is intended for students in physical sciences and engineering.
To take COMP 202, students should have a solid understanding of pre-calculus fundamentals such as polynomial, trigonometric, exponential, and logarithmic functions.
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COMP 204 Computer Programming for Life Sciences (3 credits)
Overview
Computer Science (Sci) : Computer Science (Sci): Computer programming in a high level language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms, modular software design, libraries, file input/output, debugging. Emphasis on applications in the life sciences.
Terms: Fall 2024, Winter 2025
Instructors: Becerra, David (Fall) Siddiqi, Kaleem (Winter)
Co-requisite: BIOL 112
Restrictions: Not open to students who have taken or are taking COMP 202, COMP 208, or GEOG 333; not open to students who have taken or are taking COMP 206 or COMP 250.
To take COMP 204, students should have a solid understanding of pre-calculus fundamentals such as polynomial, trigonometric, exponential, and logarithmic functions.
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COMP 208 Computer Programming for Physical Sciences and
Engineering
(3 credits)
Overview
Computer Science (Sci) : Programming and problem solving in a high level computer language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms such as searching and sorting. Modular software design, libraries, file input and output, debugging. Emphasis on applications in Physical Sciences and Engineering, such as root finding, numerical integration, diffusion, Monte Carlo methods.
Terms: Fall 2024, Winter 2025
Instructors: Langer, Michael; Pr茅mont-Schwarz, Isabeau (Fall) Pr茅mont-Schwarz, Isabeau; Zammar, Chad (Winter)
3 hours
Restrictions: Not open to students who have taken or are taking COMP 202, COMP 204, orGEOG 333; not open to students who have taken or are taking COMP 206 or COMP 250.
COMP 202 is intended as a general introductory course, while COMP 208 is intended for students with sufficient math background and in (non-life) science or engineering fields.
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COMP 250 Introduction to Computer Science (3 credits)
Overview
Computer Science (Sci) : Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics.
Terms: Fall 2024, Winter 2025
Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)
Part II: 3 credits selected from:
*** Students can take either MATH 317 or COMP 350, but not both.
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COMP 350 Numerical Computing (3 credits) ***
Overview
Computer Science (Sci) : Computer representation of numbers, IEEE Standard for Floating Point Representation, computer arithmetic and rounding errors. Numerical stability. Matrix computations and software systems. Polynomial interpolation. Least-squares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations.
Terms: Fall 2024
Instructors: Chang, Xiao-Wen (Fall)
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MATH 314 Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Terms: Fall 2024, Winter 2025
Instructors: Martine, Gabriel (Fall) Borthwick, Jack Anthony (Winter)
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MATH 315 Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2024, Winter 2025
Instructors: Paquette, Courtney (Fall) Kamran, Niky (Winter)
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MATH 316 Complex Variables (3 credits)
Overview
Mathematics & Statistics (Sci) : Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Terms: Fall 2024
Instructors: Kamran, Niky (Fall)
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MATH 317 Numerical Analysis (3 credits) ***
Overview
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Fall 2024
Instructors: Duchesne, Gabriel William (Fall)
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MATH 326 Nonlinear Dynamics and Chaos (3 credits)
Overview
Mathematics & Statistics (Sci) : Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Terms: Fall 2024
Instructors: Humphries, Tony (Fall)
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MATH 327 Matrix Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Terms: This course is not scheduled for the 2024-2025 academic year.
Instructors: There are no professors associated with this course for the 2024-2025 academic year.
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MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: This course is not scheduled for the 2024-2025 academic year.
Instructors: There are no professors associated with this course for the 2024-2025 academic year.
Winter
Prerequisite: MATH 141
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MATH 340 Discrete
Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Terms: Winter 2025
Instructors: Norin, Sergey (Winter)
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MATH 350 Honours Discrete Mathematics
(3 credits)
Overview
Mathematics & Statistics (Sci) : Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.
Terms: Fall 2024
Instructors: Norin, Sergey (Fall)
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MATH 378 Nonlinear Optimization
(3 credits)
Overview
Mathematics & Statistics (Sci) : Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods.
Terms: This course is not scheduled for the 2024-2025 academic year.
Instructors: There are no professors associated with this course for the 2024-2025 academic year.
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MATH 417 Linear Optimization (3 credits)
Overview
Mathematics & Statistics (Sci) : An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory.
Terms: Fall 2024
Instructors: Hoheisel, Tim (Fall)
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MATH 430 Mathematical Finance (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Terms: Winter 2025
Instructors: Kelome, Djivede (Winter)
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MATH 463 Convex Optimization (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing.
Terms: Winter 2025
Instructors: Paquette, Courtney (Winter)
Part III: 6-8 credits selected from:
+ Students can take at most one of MATH 410, MATH 420, MATH 527D1/D2 and WCOM 314.
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COMP 551 Applied Machine Learning (4 credits)
Overview
Computer Science (Sci) : Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems.
Terms: Fall 2024, Winter 2025
Instructors: Pr茅mont-Schwarz, Isabeau; Rabbany, Reihaneh (Fall) Li, Yue (Winter)
Prerequisite(s): MATH 323 or ECSE 205, COMP 202, MATH 133, MATH 222 (or their equivalents).
Restriction(s): Not open to students who have taken or are taking COMP 451, ECSE 551, MATH 462, or PSYC 560.
Some background in Artificial Intelligence is recommended, e.g. COMP-424 or ECSE-526, but not required.
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MATH 308 Fundamentals of Statistical Learning (3 credits)
Overview
Mathematics & Statistics (Sci) : Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software.
Terms: Winter 2025
Instructors: Yang, Archer Yi (Winter)
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MATH 410 Majors Project (3 credits) +
Overview
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2024, Winter 2025
Instructors: Khadra, Anmar; Nadarajah, Tharshanna; Correa, Jose Andres; Jakobson, Dmitry; Humphries, Tony; Paquette, Courtney; Sabok, Marcin; Sajjad, Alia; Khalili, Abbas (Fall) Kelome, Djivede (Winter)
Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
Requires departmental approval.
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MATH 420 Independent Study (3 credits) +
Overview
Mathematics & Statistics (Sci) : Reading projects permitting independent study under the guidance of a staff member specializing in a subject where no appropriate course is available. Arrangements must be made with an instructor and the Chair before registration.
Terms: Fall 2024, Winter 2025
Instructors: Kelome, Djivede (Fall) Choksi, Rustum (Winter)
Fall and Winter and Summer
Requires approval by the chair before registration
Please see regulations concerning Project Courses under Faculty Degree Requirements
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MATH 427 Statistical Quality Control (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
Terms: This course is not scheduled for the 2024-2025 academic year.
Instructors: There are no professors associated with this course for the 2024-2025 academic year.
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MATH 447 Introduction to Stochastic Processes (3 credits)
Overview
Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Terms: Winter 2025
Instructors: Paquette, Elliot (Winter)
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MATH 523 Generalized Linear Models (4 credits)
Overview
Mathematics & Statistics (Sci) : Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.
Terms: Winter 2025
Instructors: Steele, Russell (Winter)
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MATH 524 Nonparametric Statistics (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.
Terms: Fall 2024
Instructors: Genest, Christian (Fall)
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MATH 525 Sampling Theory and Applications (4 credits)
Overview
Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Terms: Winter 2025
Instructors: Dagdoug, Mehdi (Winter)
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MATH 527D1 Statistical Data Science
Practicum (3 credits) +
Overview
Mathematics & Statistics (Sci) : The holistic skills required for doing statistical data science in practice. Data science life cycle from a statistics-centric perspective and from the perspective of a statistician working in the larger data science environment. Group-based projects with industry, government, or university partners. Statistical collaboration and consulting conducted in coordination with the Data Science Solutions Hub (DaS^2H) of the Computational and Data Systems Initiative (CDSI).
Terms: Fall 2024
Instructors: Correa, Jose Andres; Kolaczyk, Eric (Fall)
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MATH 527D2 Statistical Data Science
Practicum (3 credits) +
Overview
Mathematics & Statistics (Sci) : See MATH 527D1 for course description.
Terms: Winter 2025
Instructors: Correa, Jose Andres; Kolaczyk, Eric (Winter)
Corequisites: MATH 423
No credit will be given for this course unless both MATH 527D1 and MATH 527D2 are successfully completed in consecutive terms
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MATH 545 Introduction to Time Series Analysis (4 credits)
Overview
Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Terms: Winter 2025
Instructors: Stephens, David (Winter)
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MATH 556 Mathematical Statistics 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution theory, stochastic models and multivariate transformations. Families of distributions including location-scale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.
Terms: Fall 2024
Instructors: Khalili, Abbas (Fall)
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MATH 557 Mathematical Statistics 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : Sufficiency, minimal and complete sufficiency, ancillarity. Fisher and Kullback-Leibler information. Elements of decision theory. Theory of estimation and hypothesis testing from the Bayesian and frequentist perspective. Elements of asymptotic statistics including large-sample behaviour of maximum likelihood estimators, likelihood-ratio tests, and chi-squared goodness-of-fit tests.
Terms: Winter 2025
Instructors: Genest, Christian (Winter)
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MATH 558 Design of Experiments (4 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to concepts in statistically designed experiments. Randomization and replication. Completely randomized designs. Simple linear model and analysis of variance. Introduction to blocking. Orthogonal block designs. Models and analysis for block designs. Factorial designs and their analysis. Row-column designs. Latin squares. Model and analysis for fixed row and column effects. Split-plot designs, model and analysis. Relations and operations on factors. Orthogonal factors. Orthogonal decomposition. Orthogonal plot structures. Hasse diagrams. Applications to real data and ethical issues.
Terms: Winter 2025
Instructors: Sajjad, Alia (Winter)
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MATH 559 Bayesian Theory and Methods (4 credits)
Overview
Mathematics & Statistics (Sci) : Subjective probability, Bayesian statistical inference and decision making, de Finetti鈥檚 representation. Bayesian parametric methods, optimal decisions, conjugate models, methods of prior specification and elicitation, approximation methods. Hierarchical models. Computational approaches to inference, Markov chain Monte Carlo methods, Metropolis鈥擧astings. Nonparametric Bayesian inference.
Terms: This course is not scheduled for the 2024-2025 academic year.
Instructors: There are no professors associated with this course for the 2024-2025 academic year.
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MATH 598 Topics in Probability and Statistics (4 credits)
Overview
Mathematics & Statistics (Sci) : This course covers a topic in probability and/or statistics.
Terms: Fall 2024, Winter 2025
Instructors: Addario-Berry, Louigi; Neslehova, Johanna (Fall) Asgharian, Masoud; Khalili, Abbas (Winter)
Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Probability and Statistics program including MATH 356. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
Restriction(s): Requires permission of the Department of Mathematics and Statistics.
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WCOM 314 Communicating Science (3 credits) +
Overview
WCOM : Production of written and oral assignments (in English) designed to communicate scientific problems and findings to varied audiences Analysis of the disciplinary conventions of scientific discourse in terms of audience, purpose, organization, and style; comparative rhetorical analysis of academic and popular genres, including abstracts, lab reports, research papers, print and online journalism.
Terms: Fall 2024, Winter 2025
Instructors: Kubler, Kyle; Olsen, Katrina; Guesgen, Mirjam (Fall) Hardin, Katherine; Kubler, Kyle (Winter)
Restriction: Not open to students who have taken CCOM 314.
